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Fairness-informed Pareto Optimization : An Efficient Bilevel Framework

Sofiane Tanji, Samuel Vaiter, Yassine Laguel

TL;DR

The paper tackles fairness in ML by addressing Pareto inefficiency of common in-processing methods. It introduces BADR, a bilevel framework that optimizes a user-specified fairness metric over the Pareto front of group losses, with guarantees under strong convexity. Two scalable single-loop algorithms, BADR-GD and BADR-SGD, solve the bilevel problem and come with convergence guarantees, including handling unbounded cross-derivatives via clipping and Lyapunov analysis. An open-source BADR toolbox is released, enabling metric-driven fair learning on large-scale datasets with multiple groups and fairness metrics. Empirical results show BADR improves targeted fairness while maintaining Pareto-efficient group performance and competitive accuracy.

Abstract

Despite their promise, fair machine learning methods often yield Pareto-inefficient models, in which the performance of certain groups can be improved without degrading that of others. This issue arises frequently in traditional in-processing approaches such as fairness-through-regularization. In contrast, existing Pareto-efficient approaches are biased towards a certain perspective on fairness and fail to adapt to the broad range of fairness metrics studied in the literature. In this paper, we present BADR, a simple framework to recover the optimal Pareto-efficient model for any fairness metric. Our framework recovers its models through a Bilevel Adaptive Rescalarisation procedure. The lower level is a weighted empirical risk minimization task where the weights are a convex combination of the groups, while the upper level optimizes the chosen fairness objective. We equip our framework with two novel large-scale, single-loop algorithms, BADR-GD and BADR-SGD, and establish their convergence guarantees. We release badr, an open-source Python toolbox implementing our framework for a variety of learning tasks and fairness metrics. Finally, we conduct extensive numerical experiments demonstrating the advantages of BADR over existing Pareto-efficient approaches to fairness.

Fairness-informed Pareto Optimization : An Efficient Bilevel Framework

TL;DR

The paper tackles fairness in ML by addressing Pareto inefficiency of common in-processing methods. It introduces BADR, a bilevel framework that optimizes a user-specified fairness metric over the Pareto front of group losses, with guarantees under strong convexity. Two scalable single-loop algorithms, BADR-GD and BADR-SGD, solve the bilevel problem and come with convergence guarantees, including handling unbounded cross-derivatives via clipping and Lyapunov analysis. An open-source BADR toolbox is released, enabling metric-driven fair learning on large-scale datasets with multiple groups and fairness metrics. Empirical results show BADR improves targeted fairness while maintaining Pareto-efficient group performance and competitive accuracy.

Abstract

Despite their promise, fair machine learning methods often yield Pareto-inefficient models, in which the performance of certain groups can be improved without degrading that of others. This issue arises frequently in traditional in-processing approaches such as fairness-through-regularization. In contrast, existing Pareto-efficient approaches are biased towards a certain perspective on fairness and fail to adapt to the broad range of fairness metrics studied in the literature. In this paper, we present BADR, a simple framework to recover the optimal Pareto-efficient model for any fairness metric. Our framework recovers its models through a Bilevel Adaptive Rescalarisation procedure. The lower level is a weighted empirical risk minimization task where the weights are a convex combination of the groups, while the upper level optimizes the chosen fairness objective. We equip our framework with two novel large-scale, single-loop algorithms, BADR-GD and BADR-SGD, and establish their convergence guarantees. We release badr, an open-source Python toolbox implementing our framework for a variety of learning tasks and fairness metrics. Finally, we conduct extensive numerical experiments demonstrating the advantages of BADR over existing Pareto-efficient approaches to fairness.
Paper Structure (47 sections, 29 theorems, 149 equations, 8 figures, 3 tables, 2 algorithms)

This paper contains 47 sections, 29 theorems, 149 equations, 8 figures, 3 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Multi-objective optimization
  3. Efficient Fair Learning
  4. Bilevel Optimization
  5. Fairness through a Pareto lens
  6. Inefficiency of fairness by regularization approaches
  7. Scalarization and the weighted-sum method
  8. Minmax fairness and fairness risk measures as robust scalarizations
  9. badr : an optimal Pareto-efficient approach to group fairness
  10. Large scale methods
  11. Algorithms
  12. Convergence analysis
  13. Open-source software
  14. Interface
  15. Data
  16. ...and 32 more sections

Key Result

Proposition 2

Let $\lambda \in \Delta_{S}$ be fixed. Any solution $w_\lambda$ of eq:scalazized_problem is Pareto-efficient for the multi-objective problem eq:MOproblem. Conversely, if the group losses $F_{a}$ are convex and at least one of them is strictly convex, then any Pareto efficient point for eq:MOproblem

Figures (8)

  • Figure 1: Illustration of the impact of fairness regularization on Pareto efficiency for a logistic regression task evaluated on three subsamples of the ACSEmployment dataset dataset_folktables. The first row reports the group-wise losses for the two sensitive groups (male vs. female). The two curves correspond to the Pareto front and the regularization path induced by the fairness-by-penalization approach, respectively. The second row reports the values of the considered fairness metric (individual fairness metric_kearns) on the Pareto front, together with the performance of several fairness Pareto-efficient methods compared against badr.
  • Figure 2: Overview of the badr package modules.
  • Figure 3: Performance profiles comparing SLSQP, Frank-Wolfe, and Trust-Region methods for achieving ${{\mathcal{F}}\text{air}}_{\text{best}} + \varepsilon$ across multiple tolerance levels. The vertical axis represents the fraction of instances solved, while the horizontal axis shows the factor $\tau$ of wall-clock time relative to the fastest algorithm. Higher curves indicate superior algorithm efficiency. Rightward-extending curves identify instances where algorithms demonstrate slower convergence relative to the optimal method.
  • Figure 4: (Top): Median wall-clock time (solid) with 25% and 75% interquartile ranges (shaded) computed over successful runs across five US states for SLSQP, Frank-Wolfe, and the trust-region method to first reach a fairness value of $10^{-4}$, as a function of the number of sensitive groups. (Bottom): Success rate of each method over the seven chosen states as a function of the number of sensitive groups.
  • Figure 5: Runtime scaling of badr-sgd and SLSQP with dataset size (mean $\pm$ standard deviation over 5 seeds).
  • ...and 3 more figures

Theorems & Definitions (57)

  • Definition 1: Pareto Efficiency
  • Proposition 2: See geoffrion1968proper
  • Proposition 3
  • Theorem 4
  • Remark 5
  • Remark 6
  • Theorem 7
  • Remark 8
  • Remark 9
  • Remark 10
  • ...and 47 more